Energy staggering parameters in nuclear magnetic rotational bands

The systematics of energy staggering for the magnetic rotational bands with $M1$ and $E2$ transition properties strictly consistent with the features of good candidates of magnetic rotational bands in the $A\sim80$, 110, 130 and 190 mass regions are presented. The regularities exhibited by these bands concerning the staggering parameter which increases with increasing spin are in agreement with the semiclassical description of shears mechanism. In addition, the abnormal behaviours in the backbend regions or close to band termination have also been discussed. Taking the magnetic dipole bands with same configuration in three $N=58$ isotones, i.e., $^{103}$Rh, $^{105}$Ag, and~$^{107}$In, as examples, the transition from chiral rotation to magnetic rotation with the proton number approaching $Z=50$ is presented. Moreover, the self-consistent tilted axis cranking and principle axis cranking relativistic mean-field theories are applied to investigate the rotational mechanism in dipole band of $^{105}$Ag.